A number of theorems including weak duality theorem, duality theorem, unboundedness theorem, and existence theorem are presented in the chapter to show the relations between the primal and the dual problems. The chapter also describes how duality relations in linear programming can be used in ...
本文将从离散空间上的KP开始讨论,此时KP是一个标准线性规划(linear programming)问题(而这正是线性规划的起源),可以通过求解其对偶问题(dual problem)解决。接下来会类比到一般情况(连续空间)的“对偶问题”,并用一些凸分析技巧表示出最低耗费。 (本文翻译自我自己的笔记,可能有数学/术语错误或笔误,敬请读者指正。)...
Some closedness criteria for the linear image of a closed convex cone are studied in [25], and the results therein allow to obtain the necessary conditions for a conic linear system to satisfy uniform LP duality (Theorem 1 in [22]). If the cone defining this system is nice, then these...
This is an alternative characterization to the one provided in [7, Theorem 1]. Using this characterization, the ALD of an MIP can be viewed as a traditional LD in a lifted space. 2. We give an alternative proof for the asymptotic zero duality gap property of ALD for MIPs when the ...
On the Theory of Semi-Infinite Programming and a Generalization of the Kuhn-Tucker Saddle Point Theorem for Arbitrary Convex Functions We first present a survey on the theory of semi-infinite programming as a generalization of linear programming and convex duality theory. By the pairing of a finit...
Oh also, you can prove that the solutions to discrete optimal transport are "sparse" i.e there always exist a solution with at most N+MN+M non zero coefficients (it's a consequence of Dubins theorem, I can give further details if you're interested). Another interesting things is the ...
LinearProgramming–Duality OtherDualitytopics: •WeakDualitytheorem •StrongDualitytheorem •Complementaryslackness •Dualsimplexmethod DualrelationshipDualrelationship Dualrelationship(cont)Dualrelationship(cont) LinearProgramming–Duality RelationshipbetweentheprimalandtheDual: PrimalProblem (orDualProblem) DualPro...
he found a dual for this problem. The authors generalize this result further by proving a duality theorem which includes as special cases a great variety of choices of norms in the terms of the Fermat-Weber sum. The theorem is proved by applying a general duality theorem of Rockafellar. As...
In this paper we consider the duality gap functiongthat measures the difference between the optimal values of the primal problem and of the dual problem in linear programming and in linear semi-infinite programming. We analyze its behavior when the data defining these problems may be perturbed, ...
A large chunk of the work in SVMs is converting the original, geometric problem statement, that of maximizing the margin of a linear separator, into a form suitable for this theorem. We did that last time. However, the conditions of this theorem also provide the structure for a more ...